Finite-Temperature Phase Diagram of Hard-Core Bosons in Two Dimensions

Abstract

We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3 He.A nearly universal feature of strongly correlated systems is a phase transition between a correlation-induced insulating phase with localized charge carriers, to an itinerant phase. High temperature superconductors [1], manganites [2] and the controversial two dimensional (2D) "metal-insulator-transition" [3] are just a few examples of this phenomenon. The 2D hard-core boson Hubbard model provides the simplest example of such a transition from a correlation-induced charge density wave insulator near half filling to a superfluid (SF). It is a prototypical model for preformed Cooper pairs [4], of spin flops in anisotropic quantum magnets [5,6], of SF Helium films [7] and of supersolids [8,9].In simulations on this model, which does not suffer from the negative sign problem of fermionic simulations, we can investigate some of the pertinent questions about such phase transitions: what is the order of the quantum phase transitions in the ground state and the finite temperature phase transitions? Are there special points with dynamically enhanced symmetry [10]? Can there be coexistence of two types of order (such as a supersolidcoexisting solid and superfluid order)? Answers to these questions provide insight also for the other problems alluded to above.The Hamiltonian of the hard-core boson Hubbard model we study iswhere a † i (a i ) is the creation (annihilation) operator for hard-core bosons, n i = a † i a i the number operator, V the nearest neighbor Coulomb repulsion and µ the chemical potential. This model is equivalent to an anisotropic spin-1/2 XXZ model with J z = V and |J xy | = 2t in a magnetic field h = 2V − µ. The zero field (and zero magnetization m z = 0) case of the spin model corresponds to the half filled bosonic model (density ρ = m z = 1/2) at µ = 2V . Throughout this Letter we will use the bosonic language, and refer to the corresponding quantities in the spin model where appropriate. Due to the absence of efficient Monte Carlo algorithms for classical magnets in a magnetic field there are still many open questions even in the classical version of this model, which was only studied by a local update method [11].In Fig. 1 we show the ground-state phase diagram [6,9,12]. For dominating chemical potential µ the system is in a band insulating state (ρ = 0 and ρ = 1 respectively), while it shows staggered checkerboard charge order (ρ = 1/2) for dominating repulsion V . These solid phases are separated from each other by a SF. Earlier in...

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

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Topological phase separation in a two-dimensional quantum lattice Bose-Hubbard system away from half-filling

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Drude weight in hard-core boson systems: Possibility of a finite-temperature ideal conductor

“…One of the frontiers of quantum condensed matter physics is to explore quantum phases of Bosons in two-dimensions which are not superfluids. Lattice models of interacting bosons in two dimensions, such as Bose Hubbard model, which have been studied in past primarily as models for Josephson junction arrays [1] and in context of optical lattice experiments [2] and hard core bosons, which have been studied in context of the pseudogap phase of high T c superconductors [3], are known to have insulating and superfluid phases [4,5]. In some cases coexistence of charge density wave (CDW) order and superfluidity, which is known as the supersolid (SS) phase, is also seen [5][6][7][8][9][10].…”